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In the world of early childhood math, there are some things most of us know. We know that we need to teach things like colors, shapes, numbers, counting, sorting, patterning, and graphing. And depending on the age you teach, addition and subtraction are probably on that list as well. And we teach those things really well. But then, years down the road, the very same kids who mastered all of those basic skills in pre-k, kinder, and 1st grade are now struggling in math and no one understands why. When a second grader is struggling with place value, a third grader is struggling with multiplication, or a fourth grader is struggling with finding area, there is one common factor that was probably missed during the early years: decomposing numbers.

## What Is Decomposing Numbers?

Decomposing numbers is the ability to break a number into smaller parts. It depends on the conceptual understanding that any number can be represented in parts. It is based on part-part-whole relationships, and it is a critical piece in developing number sense. It provides kiddos with the foundation they need to understand addition, subtraction, and how they relate to each other. It is also critical to kiddos being successful later with concepts like place value, multiplication, division, area, and higher level problem solving. Decomposing numbers is something our kiddos need to be able to do with automaticity at a conceptual level. They need to understand the concept of decomposing numbers, and they need to be able to apply that understanding in different situations and different ways so that they have flexibility with their number sense.

To put it simply: bigger numbers are combinations of smaller numbers, and our kiddos need to be able break them down and put them together. For example 6 can be broken down into different pairs of numbers: 0 & 6, 1 & 5, 2 & 4, and 3 & 3. And our youngest learners need to have a firm grasp on this long before we ever expect them to write an addition sentence or memorize a subtraction fact. They need to And that’s where we mess up. We go straight from counting to adding and subtracting without giving our kiddos time to play with and develop the concept of decomposing.

## How Do I Teach Decomposing?

The best way to teach your kiddos to decompose numbers is to give them as many experiences with it as possible. Skills that are conceptual in nature are only developed through experiences… and a LOT of them! In other words, it’s not a simple procedure you can teach like when you teach how to write a number or how to count. Numbers are always written the same way, and you model it, teach it, and have your kiddos practice it the same way over and over until they get. The counting sequence is always the same. You model it, teach it, and have your kiddos practice it until they get it. But when we’re teaching flexible skills, we have to teach them in flexible ways. So, to teach decomposing numbers, we need to give our kiddos as many different opportunities as possible to play with these different combinations of numbers.

We lay the foundation in preschool and pre-k with manipulatives. Lots and LOTS of manipulatives! Some of my absolute favorites are Unifix cubes, counting bears, two-sided counters, and ALL the mini-erasers from Target! (I may have a slight obsession with these!) In kinder, we start putting a little more structure to it by adding in written representations of the number combinations. And in first grade, we transition into written addition and subtraction facts. It’s a definite progression, and the grade level suggestions are just that… suggestions. Ultimately, YOU are the expert on your kiddos! And YOU will need to decide when they are ready for the next level of learning!

I’m putting together a series of blog posts to make this a little easier for you! They will take your through how to build a foundation in pre-k and how to use my Number Pockets system to help your kinders and firsties fully develop the concept of decomposing numbers! Just use the links below to read through the entire series! (Links will become live as posts are added! But for now, you can see what’s coming!)

Decomposing Numbers: Building the Foundation in Pre-K

Number Pockets: Getting Started

Number Pockets: Using the Games

Number Pockets: Organization and Record Keeping

In the meantime, I highly recommend reading up on teaching math in the early childhood grades! Pretty much the only reading I EVER do is professional reading because I’m just a nerd like that! So, I’ve got a few fantastic recommendations for you!

The Young Child and Mathematics by Juanita V. Copley
This one is published by NAEYC. I absolutely ADORE anything and everything published by the NAEYC!! This book is a great combination of theory and practical ideas. It covers all the major mathematical strands and has some GREAT information!

Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education by Heinemann
This book has SO MUCH great information! It covers child development as it relates to math, early childhood math theory, classroom set up, and a ton of practical ideas for teaching your kiddos!

Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades Pre-K-2 by John Van de Walle
Being developmentally appropriate is a BIG deal for me! And this book is FULL of information and ideas to make sure your thinking and teaching are always in line with developmentally appropriate practices!

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